Question

solve for v, where v is a real number.
-2 + \sqrt{v - 5} = 2
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.

Explanation:

Step1: Isolate the square root

Add 2 to both sides of the equation $-2 + \sqrt{v - 5} = 2$ to get $\sqrt{v - 5} = 2 + 2$.
$\sqrt{v - 5} = 4$

Step2: Eliminate the square root

Square both sides of the equation to eliminate the square root: $(\sqrt{v - 5})^2 = 4^2$.
$v - 5 = 16$

Step3: Solve for v

Add 5 to both sides of the equation: $v = 16 + 5$.
$v = 21$

Step4: Check the solution

Substitute $v = 21$ back into the original equation: $-2 + \sqrt{21 - 5} = -2 + \sqrt{16} = -2 + 4 = 2$, which matches the right - hand side. So $v = 21$ is a valid solution.

Answer:

21